I agree. Air in the lines will compress quite a bit more than water, and that will make the pump take longer to cycle off. You may need to run the hot water for several minutes to purge air out of the water heater.

You may have insufficient flow from the pump to properly get rid of all the air; hooking up to city water will help in that case. Bleed the air from the lines as you'd bleed your brakes - start with the faucet/tap closest to the pump (in terms of plumbing runs) and work towards the furthest. Don't forget to open the drain taps as well; they might have some dead end runs that could retain air.